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A342631
Number of Hamiltonian paths (or Gray codes) on n-cube with the origin as the starting node, up to a permutation of the coordinates.
1
1, 1, 3, 238, 48828036
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Hypercube Graph
FORMULA
a(n) = A003043(n) / n!.
EXAMPLE
For n=2, the two Hamiltonian paths of the square that start at (0,0), i.e.,
(0,0) -->-- (1,0) (0,0) (1,0)
| | |
V and V ^
| | |
(0,1) --<-- (1,1) (0,1) -->-- (1,1),
only account for one, as one is obtained from the other by the x <-> y permutation; so a(2) = 1.
PROG
(C) See link.
CROSSREFS
Sequence in context: A278318 A103062 A157723 * A142730 A264549 A024044
KEYWORD
nonn,hard,more
AUTHOR
Luc Rousseau, May 24 2021
STATUS
approved